Question: A group of adults and kids went to see a movie. Tickets cost $$8.50$ each for adults and $$2.50$ each for kids, and the group paid $$49.00$ in total. There were $2$ fewer adults than kids in the group. Find the number of adults and kids in the group.
Solution: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${8.5x+2.5y = 49}$ ${x = y-2}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-2}$ for $x$ in the first equation. ${8.5}{(y-2)}{+ 2.5y = 49}$ Simplify and solve for $y$ $ 8.5y-17 + 2.5y = 49 $ $ 11y-17 = 49 $ $ 11y = 66 $ $ y = \dfrac{66}{11} $ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into ${x = y-2}$ to find $x$ ${x = }{(6)}{ - 2}$ ${x = 4}$ You can also plug ${y = 6}$ into ${8.5x+2.5y = 49}$ and get the same answer for $x$ ${8.5x + 2.5}{(6)}{= 49}$ ${x = 4}$ There were $4$ adults and $6$ kids.